Electric Potential Profile Research Articles

Incorporating ion-specific van der Waals and soft repulsive interactions in the Poisson-Boltzmann theory of electrical double layers.

Electrical double layers (EDLs) arise when an electrolyte is in contact with a charged surface, and are encountered in several application areas including batteries, supercapacitors, electrocatalytic reactors, and colloids. Over the last century, the development of Poisson-Boltzmann (PB) models and their modified versions have provided significant physical insight into the structure and dynamics of the EDL. Incorporation of physics such as finite-ion-size effects, dielectric decrement, and ion-ion correlations has made such models increasingly accurate when compared to more computationally expensive approaches such as molecular simulations and classical density functional theory. However, a prominent knowledge gap has been the exclusion of van der Waals (vdW) and soft repulsive interactions in modified PB models. Although short-ranged as compared to electrostatic interactions, we show here that vdW and soft repulsive interactions can play an important role in determining the structure of the EDL via the formation of a Stern layer and in modulating the differential capacitance of an electrode in an electrolyte. To this end, we incorporate ion-ion and wall-ion vdW attraction and soft repulsion via a 12-6 Lennard-Jones (LJ) potential, resulting in a modified PB-LJ approach. The wall-ion LJ interactions were found to have a significant effect on the electrical potential and concentration profiles, especially close to the wall. However, ion-ion LJ interactions do not affect the EDL structure at low bulk ion concentrations (<1 M). We also derive dimensionless numbers to quantify the impact of ion-ion and wall-ion LJ interactions on the EDL. Furthermore, in the pursuit of capturing ion-specific effects, we apply our model by considering various ions such as Na, K+, Mg2+, Cl-, and SO42-. We observe how varying parameters such as the electrolyte concentration and electrode potential affect the structure of the EDL due to the competition between ion-specific LJ and electrostatic interactions. Lastly, we show that the inclusion of vdW and soft repulsion interactions, as well as hydration effects, leads to a better qualitative agreement of the PB models with experimental double-layer differential capacitance data. Overall, the modified PB-LJ approach presented herein will lead to more accurate theoretical descriptions of EDLs in various application areas.

Decoupling of dust cloud and embedding plasma for high electron depletion in nanodusty plasmas

In recent years nanoparticles have become key technological products, e.g., as coatings with tunable optical gap in third generation solar cells, as nanocrystals for photonic applications, and as pharmaceutical nanocarriers. In particle sources, that use reactive, nanodusty plasmas, a high dust density changes the properties of the dusty plasma compared to a dust free plasma considerably, as electron depletion leads to a reduced number of free electrons. This is called the Havnes effect and was central for the understanding of the famous spokes in Saturns rings. We see here, that it is also important for technological applications. Using self excited dust density waves (DDW) as a diagnostic tool, we completely characterize an argon discharge with embedded amorphous hydrocarbon nanoparticles of different size and density. The results show, that electron depletion governs the charge of dust grains, while the size of the particles has only a weak influence. The ion density and electric potential profile are almost independent of both, dust size as well as dust density. This suggests, that the rf generated plasma and the dust cloud seem to coexist and coupling of both is weak.

Transplantation of fragments from different planaria: A bioelectrical model for head regeneration

Head-tail planaria morphologies are influenced by the electric potential differences across the animal’s primary axis, as evidenced e.g. by voltage-sensitive dyes and functional experiments that create permanent lines of 2-headed but genetically wild-type animals. However, bioelectrical and biochemical models that make predictions on what would happen in the case of spatial chimeras made by tissue transplantation from different planaria (different species and head shapes) are lacking. Here, we use a bioelectrical model to qualitatively describe the effects of tissue transplantation on the shape of the regenerated head. To this end, we assume that the cells may have distinct sets of ion channels and ascribe the system outcome to the axial distributions of average cell potentials over morphologically relevant regions. Our rationale is that the distributions of signaling ions and molecules are spatially coupled with multicellular electric potentials. Thus, long-time downstream transcriptional events should be triggered by short-time bioelectrical processes. We show that relatively small differences between the ion channel characteristics of the cells could eventually give noticeable changes in the electric potential profiles and the expected morphological deviations, which suggests that small but timely bioelectrical actions may have significant morphological effects. Our approach is based on the observed relationships between bioelectrical regionalization and biochemical gradients in body-plan studies. Such models are relevant to regenerative, developmental, and cancer biology in which cells with distinct properties and morphogenetic target states confront each other in the same tissue.

Electric Potential Profiles in a Model Single-Path Electrodialysis Unit.

Electrodialysis is an important electromembrane separation process anticipated to play a significant role in developing future technologies. It produces ion-depleted and ion-concentrated product streams, intrinsically suggesting the formation of spatial gradients of relevant quantities. These quantities affect local conditions in an electrodialysis unit. To investigate the spatial distribution of electric potentials, we constructed a model electrodialysis system with a single diluate channel that included ports for inserting reference electrodes measuring potential profiles. We validated our system and measurement methods in a series of control experiments under a solution flow rate of 250 µL/min and current densities between 10 and 52 A/m2. The collected data showed that the electric potential in the diluate channel did not change in the vertical direction (direction of gravity force), and only minimally varied in the diluate channel center in the flow direction. Although we could not reconstruct the potential profile within ion-depleted layers due to the resolution of the method, we found appreciable potential variation across the diluate channel. The most significant potential drops were localized on the membranes with the developed ion-depleted zones. Interestingly, these potential drops abruptly increased when we applied current loads, yielding almost complete desalination. The increase in the resistance accompanied by relatively large fluctuations in the measured potential indicated the system transition into limiting and overlimiting regions, and the onset of overlimiting convection.

Conceptual design of a heavy ion beam probe for the QUEST spherical tokamak.

A heavy ion beam probe (HIBP) has been designed for the QUEST spherical tokamak to measure plasma turbulence and the profiles of electric potential profiles. Using a cesium ion beam with an energy of several 10keV, the observable region covers most of the upper half of the plasma. Although the probe beam is deflected by the poloidal magnetic field produced by plasma current and poloidal coil currents, it can be detected under plasma current up to 150kA by modifying the trajectories with two electrostatic sweepers. According to the numerical estimation of the intensity of the detected beam, sufficient signal intensity for measuring plasma turbulence can be obtained over almost the measurable area when the electron density is up to 1 × 1019 m-3, which is larger than the cut-off density of electron cyclotron heating in QUEST. The performance of the designed HIBP is sufficient to explore the mechanisms of heat and particle transport in magnetically confined plasmas, including the influence of plasma wall interactions, which is a goal of the QUEST project.

Transient Analysis of the Electro-Osmotic Flow of Multilayer Immiscible Maxwell Fluids in an Annular Microchannel

This work investigates the transient multilayer electro-osmotic flow of viscoelastic fluids through an annular microchannel. The dimensionless mathematical model of multilayer flow is integrated by the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, the rheological Maxwell model, initial conditions, and the electrostatic and hydrodynamic boundary conditions at liquid-liquid and solid-liquid interfaces. Although the main force that drives the movement of fluids is due to electrokinetic effects, a pressure gradient can also be added to the flow. The semi-analytical solution for the electric potential distribution and velocity profiles considers analytical techniques as the Laplace transform method, with numerical procedures using the inverse matrix method for linear algebraic equations and the concentrated matrix exponential method for the inversion of the Laplace transform. The results presented for velocity profiles and velocity tracking at the transient regime reveal an interesting oscillatory behavior that depends on elastic fluid properties via relaxation times. The time required for the flow to reach steady-state is highly dependent on the viscosity ratios and the dimensionless relaxation times. In addition, the influence of other dimensionless parameters on the flow as the electrokinetic parameters, zeta potentials at the walls, permittivity ratios, ratio of pressure forces to electro-osmotic forces, number of fluid layers, and annular thickness are investigated. The findings of this study have significant implications for the precise control of parallel fluid transport in microfluidic devices for flow-focusing applications.

Continuous Ion Separations Using Non-Faradaic Capacitive AC Ratcheting

Traditional electrochemical separations processes require Faradaic reactions for sustained currents. We discovered that this limitation can be overcome by oscillating the applied potential across an ion-permeable material that has an asymmetric electric potential profile. We demonstrated this phenomenon for the first time using a flashing ratchet consisting of a nanoporous anodized aluminum oxide membrane infiltrated with salt water and containing metallic contacts on either side. When a symmetric +/-300 mV square-wave potential was applied to the metallic contacts at a frequency of ~100 Hz, an open-circuit potential as large as ~50 mV was observed between Ag/AgCl electrodes immersed in the chloride-containing electrolyte and positioned across the membrane. While this open-circuit potential was determined to be a consequence of net ionic polarization, additional electrochemical data were also consistent with transport of neutral salt across the membrane via a proposed ambipolar transport mechanism. In comparison, application of a DC potential bias resulted in non-Faradaic charging, and a near-zero long-time open-circuit potential. Moreover, high ionic strengths and large pore sizes diminished ratcheting behavior, consistent will more complete screening of surface charges in the nanopores. Collectively, this work represents a new paradigm for direct ion pumping and salt separations that requires no Faradaic reactions or additional transport pathway for ions or electrons.

Accurate Solutions to Non-Linear PDEs Underlying a Propulsion of Catalytic Microswimmers

Catalytic swimmers self-propel in electrolyte solutions thanks to an inhomogeneous ion release from their surface. Here, we consider the experimentally relevant limit of thin electrostatic diffuse layers, where the method of matched asymptotic expansions can be employed. While the analytical solution for ion concentration and electric potential in the inner region is known, the electrostatic problem in the outer region was previously solved but only for a linear case. Additionally, only main geometries such as a sphere or cylinder have been favoured. Here, we derive a non-linear outer solution for the electric field and concentrations for swimmers of any shape with given ion surface fluxes that then allow us to find the velocity of particle self-propulsion. The power of our formalism is to include the complicated effects of the anisotropy and inhomogeneity of surface ion fluxes under relevant boundary conditions. This is demonstrated by exact solutions for electric potential profiles in some particular cases with the consequent calculations of self-propulsion velocities.

Design of an omnidirectional camouflage device with anisotropic confocal elliptic geometry in thermal-electric field

SummaryThe designed confocal elliptical core-shell structure can realize the omnidirectional camouflage effect without disturbing temperature and electric potential profiles as the directions of heat flux and electric current change. Based on the anisotropy of the confocal ellipse, the anisotropic effective parameters of the confocal elliptical core-shell structure are derived under different heat flux and electric current launching. Then, the matrix material should be anisotropic as the effective parameters to satisfy the omnidirectional camouflage effect, which is demonstrated numerically. In addition, we present a composite structure to realize the anisotropic matrix. The experimental results show that the camouflage device embedded in the composite structure can eliminate the scattering caused by the elliptical core under different directions of heat flux and electric current, thus achieving the omnidirectional thermal-electric camouflage effect experimentally. The omnidirectional camouflage effect in thermal and electric fields can greatly widen the application fields of this device with anisotropic geometry.

Evaluating bioelectrochemically-assisted constructed wetland (METland®) for treating wastewater: Analysis of materials, performance and electroactive communities

METland® technology consists of a bioengineering strategy for treating wastewater by integrating microbial electrochemical concepts into constructed wetland systems to enhance pollutants removal. In this context, we have constructed planted (Iris sibirica) biofilters to assess the impact of different electrically conductive bed materials (electroconductive coke, electroconductive biochar, non-electroconductive biochar and gravel) by analyzing the (i) wastewater treatment efficiency (COD and nitrogen removal), (ii) bioelectrochemical response, and (iii) diversity of microbial communities. Electrically conductive materials outperformed non-conductive ones allowing removal rates as high as 175–180 gCOD/bed*m3 day capable to support footprint as low 0.4 m2/pe. In contrast, the highest nitrogen removal rates were achieved with non-conductive biochar in presence of plants (80 %) regardless the anoxic conditions of the assay. This was confirmed by the presence of annamox bacteria like Planctomycetes. Furthermore, the presence of a marked electric potential profile along the bed height in electroconductive materials together with redox pairs (cyclic voltammetry analysis) demonstrated an effective electron flow from bottom to uppermost layers of the bed (geoconductor mechanism). In electroconductive biochar, such effective conductivity-based model co-exists with a geobattery mechanism due to presence of electroactive phenolic and carbonyl/quinone groups and/or microporosity. Microbial biodiversity analysis revealed the impact of plants just at the upper layers of the biofilters where roots and Rhizobium predominate. Bacteria from genus Clostridium were dominant in gravel inert material; in contrast, bacteria from genus Geobacter (12%) and Trichococcus (30%) outcompete the rest of communities for an effective colonization of carbonaceous beds, suggesting their main role as part of the electrosyntrophies mechanism after METland®.

The Identification of Electrical Properties of Acupuncture Points for Asthma Diagnosis

The aim of this research is to identify the electrical potential profile on the acupoint betwen healthy people and the patient of asthma. The raw data has taken by recording the electrical potential profile on the acupoints: Feishu, Pishu, and Shenshu from 10 healthy women and the 10 women with asthma attain the age of 20-30 years old based on the second data observation at the Local Government Clinic Kalijudan, Surabaya. Potential profile of the organs were the electrical signals form. It was achieved by the result of electrical potential which was based time recording. Recording time was done for 180 second. The results couldn't be differentiated significantly, so it needs the other signals processing with FFT analyze method with cutting as the data frames. It was done every 5 second. Based on the result of analyzing the amplitude of each frequency group, the significant differences are on the acupoint Shenshu : 0-5 Hz with p= 0.001, on the acupoint Phishu 148-152 Hz with p= 0.010, on the acupoint Feishu for frequency 198-203 Hz with p= 0.004 and on the acuponit Phishu p=0.011, for frequency 348-352 Hz on the acupoint Feishu and Shenshu have both value is p= 0,004 and 398-402 Hz with p=0,009 on the acupoint Phishu. According to the preference, it was found that the electrical potential profile on the acupoints of the healthy people has lower amplitude than the people with asthma. Then, the analyze of electrical potential profile on the acupoints can be used for asthma diagnose.

An accurate reduced-dimension numerical model for evolution of electrical potential and ionic concentration distributions in a nano-scale thin aqueous film

The numerical modelling of ionic diffusive transport through a charged thin film of electrolyte is mathematically and computationally complex due to the strongly coupled hydrodynamics and electrochemical interactions. Generally, simulations are performed by solving the Poisson equation together with the Nernst-Planck flux formula to model electrochemical processes in electro-diffusion problems. One important application of these system of equations to study the interaction of ionic diffusion and thin film hydrodynamics in petroleum engineering. However, due to the highly nonlinear and coupled equations the computational costs are heavy and very often limited to simulations in two-dimensional geometries. In this article, we have developed an equivalent one-dimensional electro-diffusive transport model based on mathematical averaging of 2D equations to reduce the computational time. Doing so, the computational time is improved substantially and simulation of much larger domain sizes which are required to study and interpret the experimental results is shown to be feasible. We have shown the high accuracy of the developed model by comparing the electric potential and concentration profiles of the developed model against the original 2D simulations. The developed approach reduces the computational effort by over 200 times without losing accuracy.

An analytical study on electroosmotic flow within a microchannel disregarding the Debye–Huckel approximation

The present work investigates analytically an electroosmotic flow (EOF) of a Newtonian liquid in a microchannel between two parallel plates. Homotopy perturbation method (HPM) is used to solve the constitutive governing equations. The Poisson-Boltzmann equation for electrical potential distribution is considered. Present work disregards the Debye–Huckel approximation to minimize exactness of present results. Consequently, using the electric potential profile obtained, a modified Navier–Stokes equation is solved for velocity distribution. The energy equation is also altered based on scale analysis to find temperature distribution. Finally, based on the temperature profile Nusselt number is determined. The proposed results are shown in comparison with a numerical and an established result which considers the Debye–Huckel approximation. It is seen that the present results agree well with the numerical predictions for a varied range of zeta potential. But, the established conventional method differs from the numerical result for higher range of zeta potential. Nusselt number is evaluated and shown as function of the electrokinetic length for different zeta potentials. The work finally concludes that the proposed model can be applied for predicting EOF in microchannels for wider range of zeta potential.

Electrophoresis and electric conduction in a salt-free suspension of charged particles.

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.

Scale-up and Modelling of Flow-electrode CDI Using Tubular Electrodes

A novel design for a flow-electrode capacitive deionization (FCDI) system consisting of tubular electrodes in a shell and tube heat exchanger configuration is proposed. Each electrode consists of a metallic mesh current collector along the inner circumference of a tubular ion-exchange membrane. This tubular FCDI design is suitable for scale-up as it consists of easily manufactured components which can be assembled in an array. An apparatus with 4 tubular electrodes with a large effective area (202.3 cm2) was constructed and shown to provide a high net salt (NaCl) removal rate (0.15 mg s−1 at 1.2 V applied voltage and ∼2000 mg L−1 influent total dissolved solids concentration). A computational fluid dynamics (CFD) model incorporating ion migration and transport mechanisms was developed to simulate the ion concentration and electrical potential profiles in the water channel. The results of CFD modelling highlighted the need to maximize regions of both high potential gradient and high hydraulic flow in order to achieve optimal salt removal. In brief, this study presents a new design approach for FCDI scale-up and provides a computational tool for optimization of this design and future innovative FCDI designs.

Furcated droplet motility on crystalline surfaces.

Directed liquid motion has been conventionally mediated by functionalizing chemical inhomogeneity or texturing topological anisotropy on target surfaces. Here we show the self-propulsion of droplets that furcated in well-defined directions on piezoelectric single crystals in the absence of any apparent asymmetry or external force. By selecting the crystal plane to interface with the droplets, the thermoelastic-piezoelectric interplay yields intricate electric potential profiles, enabling various forms of self-propulsion including unidirectional, bifurcated and trifurcated. This effect originates from an anisotropic crystalline structure that generates contrasting macroscopic liquid behaviours and is observed with cold/hot and volatile droplets. Intrinsically oriented liquid motions have broad applicability in processes ranging from soft matter engineering, autonomous material delivery and thermal management to biochemical analysis.

In Vivo Evaluation of Fractal Microelectrodes Towards a More Targeted and Energy‐Efficient Vagus Nerve Stimulation

Vagus nerve stimulation (VNS) is a moderately effective treatment option for intractable epilepsy, depression, and pain, with promising applications in the treatment of gastrointestinal motility disorders like gastroparesis. The wide-ranging potential indications of VNS suggest an opportunity for a better understanding of underlying neural circuits that can be targeted using microscale electrodes. However, microscale Platinum (Pt) electrodes often have limited charge injection capacity due to their high impedance. Recently, we experimentally demonstrated that microscale Pt electrodes with Vicsek fractal geometry can facilitate electrochemical charge transfer more efficiently with 57% higher cathodic charge storage capacity than conventional circular microelectrodes. Here we are investigating whether the fractal electrode may be more effective in eliciting small fibers in the vagus nerve with less energy consumption due to its enhanced charge injection capability. To evaluate the in vivo performance of these novel microelectrode designs and to determine whether these electrodes are capable of stimulating small, unmyelinated C fibers that supply the stomach, we designed a cuff electrode with an array with four pairs of fractal and circular microelectrode to explore the possibility of radial selective stimulation of vagus nerve. We determined the dimension of the cuff to be 760 μm in diameter to wrap around a rat's vagus nerve so that it can withstand the swelling of the nerve from chronic implantation. We patterned fractal microelectrode to have a geometrical surface area equivalent to that of a circle with 100 μm of diameter. Using a rat model, we have stimulated the right cervical vagus nerve with fractal/circular electrode and recorded the compound action potential (CAP) distal from the stimulation site with 5-7 mm of conduction distance or the dorsal trunk of the abdominal vagus (conduction distance: 70 mm). We used an autonomous neural control (ANC) system, which can stimulate and record from the nerve with randomized stimulus parameter combinations (pulse amplitude: 0-0.4 mA, pulse width: 0.02-1 ms). We adapted a cathode-first, alternating monophasic stimulation for the reliable suppression of stimulus artifact (pulse repetition frequency: 5 Hz). Results from right cervical VNS experiments in anesthetized rats showed that both the fractal and the circular electrodes can recruit small, myelinated Ad and B fibers to a similar degree (pulse amplitude: 0-0.4 mA, pulse width: 0.1 ms) (Figure 1.), but fractal electrodes produce a more uniform and consistent fiber recruitment profile (Figure 2.). We observed volleys within the slow conduction velocity range (< 3 m/s), which we suspect to be signals from the C-fibers. Our next plan is to obtain more experimental data to statistically identify the efficiency of various electrode designs in stimulating small fibers and to investigate the electrical potential profile of these electrodes in a biophysical model.

Impact of electroosmotic flow on a Casson fluid driven by chemical reaction and convective boundary conditions

AbstractA numerical and theoretical review of the electroosmosis flow effect on a transient state Casson fluid by natural convection stream past an exponentially accelerated plate is provided in this report. Additionally, porous medium, thermal radiation, magnetic field, electric field, ramped wall temperature and isothermal concentration are taken into consideration. The equation of Poisson–Boltzmann is used to depict the electrical potential profile within the fluid medium linearized by the Debye–Hückel implementation. Using the Laplace transform technique, the analytical solutions of momentum, energy, and concentration equations are determined. The obtained solutions of axial velocity, fluid temperature, and concentration expressions are diagrammatically revealed, and numerical results for the number of Nusselt are also obtained for critical related flow parameters. The natural convection of ramped wall temperature was also compared to the isothermal system. With the increase in Joule heating parameter, mass Grashof number, Prandtl number, and chemical reaction parameter, the velocity has been reduced for both the case of ramped and isothermal wall temperatures (RIWT). The uses of the RIWT are applicable to clean nuclear plant wastewater, food manufacturing, drilling operations, and bioengineering operations.

Identification of Composite Insulator Criticality Based on a New Leakage Current Diagnostic Index

In this article, a new method is proposed to identify the health condition of composite insulators through investigating the leakage current (LC) along with the electric potential (EP) and electric field stress (EFS) profiles. In this regard, variations of the LC harmonics and the distribution profiles of the EP and EFS are investigated through a series of experimental and simulation analyses conducted on composite insulators under various environmental and pollution conditions. Fast Fourier transform (FFT) and a COMSOL-multiphysics environment are utilized to analyze this variation. The results reveal a strong correlation between the LC harmonics and the insulator health condition. A new diagnostic criticality index based on the third to the fifth harmonic ratios of the insulator LC is proposed to quantify the composite insulator criticality and predict the likelihood of flashover occurrence. The EP and EFS analyses can be used to provide a complementary diagnosis of the insulator's health state under severe pollution and humidity conditions. The proposed analysis enables the transmission line network operator to get an insight into the insulators' functional status, thus improving the network reliability through avoiding insulator failure and adopting a proper condition-based maintenance scheme.

Mathematical model of electromigration allowing the deviation from electroneutrality.

The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern-Gouy-Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigrationconsidering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G-function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.